A novel fractional wavelet transform and its applications

The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing.However,the signal analysis capability of the former is limited in the time-frequency plane.Although the latter has overcome such limitation and can provide signal representations in the fractional domain,it fails in obtaining local structures of the signal.In this paper,a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT.The proposed transform not only inherits the advantages of multiresolution analysis of the WT,but also has the capability of signal representations in the fractional domain which is similar to the FRFT.Compared with the existing FRWT,the novel FRWT can offer signal representations in the time-fractional-frequency plane.Besides,it has explicit physical interpretation,low computational complexity and usefulness for practical applications.The validity of the theoretical derivations is demonstrated via simulations.     

一种新型分数阶小波变换及其应用

小波变换和分数Fourier变换是应用非常广泛的信号处理工具.但是,小波变换仅局限于时频域分析信号;分数Fourier变换虽突破了时频域局限能够在分数域分析信号,却无法表征信号局部特征.为此,提出了一种新型分数阶小波变换,该变换不但继承了小波变换多分辨分析的优点,而且具有分数Fourier变换分数域表征功能.与现有分数阶小波变换相比,新型分数阶小波变换可以实现对信号在时间-分数频域的多分辨分析.此外,该变换具有物理意义明确和计算复杂度低的优点,更有利于满足实际应用需求.最后,通过仿真实验验证了所提理论的有效性.     

Comparative study on classifying human activities with miniature inertial and magnetic sensors

This paper provides a comparative study on the different techniques of classifying human activities that are performed using body-worn miniature inertial and magnetic sensors. The classification techniques implemented and compared in this study are: Bayesian decision making (BDM), a rule-based algorithm (RBA) or decision tree, the least-squares method (LSM), the k-nearest neighbor algorithm (k-NN), dynamic time warping (DTW), support vector machines (SVM), and artificial neural networks (ANN). Human activities are classified using five sensor units worn on the chest, the arms, and the legs. Each sensor unit comprises a tri-axial gyroscope, a tri-axial accelerometer, and a tri-axial magnetometer. A feature set extracted from the raw sensor data using principal component analysis (PCA) is used in the classification process. A performance comparison of the classification techniques is provided in terms of their correct differentiation rates, confusion matrices, and computational cost, as well as their pre-processing, training, and storage requirements. Three different cross-validation techniques are employed to validate the classifiers. The results indicate that in general, BDM results in the highest correct classification rate with relatively small computational cost.     

分数阶Fourier域低分辨雷达飞机回波的分形特性分析与目标分类

常规低分辨雷达体制下的目标分类与辨识是雷达目标识别领域的一个研究难点。研究表明,地、海、空等雷达杂波具有分形特性,不同类型目标会对回波分形特性产生不同的影响,但在强杂波背景下,回波的分形特性更多地表现为杂波的特性。作为一种非平稳信号分析工具,分数阶Fourier变换可以有效地获取目标回波信号的细节特征并充分抑制杂波,且具有快速算法。为此,论文立足于分形及其相关理论,拟从分数阶Fourier域对常规雷达飞机目标回波的分形特性进行分析,估计和分析其分形参数,并对分数阶Fourier域回波分形特征在飞机目标分类中的应用进行探讨。研究结果表明,在最优变换阶数下,分数阶Fourier域飞机目标回波具有显著的分形特性,且充分反映了目标的特性,分形测度分析可以揭示回波的动力学演化机制,且最优变换域回波分形特征可以有效用于飞机目标的分类和识别。     

基于混合粒子群算法的小波神经网络故障诊断

针对复杂的飞控系统传感器故障类型,建立了故障诊断模型,提取了各种故障数据.构建3层小波神经网络,并提出一种改进粒子群算法--混合粒子群算法对小波神经网络进行训练,该算法使用离散粒子群算法优化小波神经网络连接结构,同时使用基本粒子群优化算法优化小波神经网络权值.将这种改进的小波神经网络算法应用于飞控系统传感器故障诊断中....     

Fuzzy clustering and enumeration of target type based on sonar returns

The fuzzy c-means (FCM) clustering algorithm is used in conjunction with a cluster validity criterion, to determine the number of different types of targets in a given environment, based on their sonar signatures. The class of each target and its location are also determined. The method is experimentally verified using real sonar returns from targets in indoor environments. A correct differentiation rate of 98% is achieved with average absolute valued localization errors of and 0.8° in range and azimuth, respectively.     

Noisy Time Series Prediction using Recurrent Neural Networks and Grammatical Inference

Financial forecasting is an example of a signal processing problem which is challenging due to small sample sizes, high noise, non-stationarity, and non-linearity. Neural networks have been very successful in a number of signal processing applications. We discuss fundamental limitations and inherent difficulties when using neural networks for the processing of high noise, small sample size signals. We introduce a new intelligent signal processing method which addresses the difficulties. The method proposed uses conversion into a symbolic representation with a self-organizing map, and grammatical inference with recurrent neural networks. We apply the method to the prediction of daily foreign exchange rates, addressing difficulties with non-stationarity, overfitting, and unequal a priori class probabilities, and we find significant predictability in comprehensive experiments covering 5 different foreign exchange rates. The method correctly predicts the directionof change for the next day with an error rate of 47.1%. The error rate reduces to around 40% when rejecting examples where the system has low confidence in its prediction. We show that the symbolic representation aids the extraction of symbolic knowledge from the trained recurrent neural networks in the form of deterministic finite state automata. These automata explain the operation of the system and are often relatively simple. Automata rules related to well known behavior such as tr end following and mean reversal are extracted.     

基于最优阶次分数阶神经网络的交通流预测

建立基于最优阶次的分数阶神经网络的动态预测模型,给出数据预处理、最优阶次优化和预测算法流程步骤,给定模型预测精确度的性能指标。分数阶神经网络是从时频两方面分析数据,比BP神经网络具有更灵活有效的函数逼近能力;针对短时数据分析,分数阶神经网络局部性与小波神经网络一致具有多分辨力,且有更强的自适应能力、更快的收敛速度和更高的预测精度。以短时交通流量数据为例进行仿真,与基于小波神经网络和BP神经网络模型的短时交通流量预测仿真比较,分析评价性能指标,结果表明分数阶神经网络最优阶次下可实现灵活快速有效的交通流量动态预测。     

Differential evolution trained wavelet neural networks: Application to bankruptcy prediction in banks

In this study, differential evolution algorithm (DE) is proposed to train a wavelet neural network (WNN). The resulting network is named as differential evolution trained wavelet neural network (DEWNN). The efficacy of DEWNN is tested on bankruptcy prediction datasets viz. US banks, Turkish banks and Spanish banks. Further, its efficacy is also tested on benchmark datasets such as Iris, Wine and Wisconsin Breast Cancer. Moreover, Garson’s algorithm for feature selection in multi layer perceptron is adapted in the case of DEWNN. The performance of DEWNN is compared with that of threshold accepting trained wavelet neural network (TAWNN) [Vinay Kumar, K., Ravi, V., Mahil Carr, & Raj Kiran, N. (2008). Software cost estimation using wavelet neural networks. Journal of Systems and Software] and the original wavelet neural network (WNN) in the case of all data sets without feature selection and also in the case of four data sets where feature selection was performed. The whole experimentation is conducted using 10-fold cross validation method. Results show that soft computing hybrids viz., DEWNN and TAWNN outperformed the original WNN in terms of accuracy and sensitivity across all problems. Furthermore, DEWNN outscored TAWNN in terms of accuracy and sensitivity across all problems except Turkish banks dataset.     

Lattice Dynamical Wavelet Neural Networks Implemented Using Particle Swarm Optimization for Spatio–Temporal System Identification

In this brief, by combining an efficient wavelet representation with a coupled map lattice model, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNNs), is introduced for spatio-temporal system identification. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimization (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the OPP algorithm, significant wavelet neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer. The resultant network model, obtained in the first stage, however, may be redundant. In the second stage, an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network. An example for a real spatio-temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework.     

The time-organized map algorithm: extending the self-organizing map to spatiotemporal signals

The new time-organized map (TOM) is presented for a better understanding of the self-organization and geometric structure of cortical signal representations. The algorithm extends the common self-organizing map (SOM) from the processing of purely spatial signals to the processing of spatiotemporal signals. The main additional idea of the TOM compared with the SOM is the functionally reasonable transfer of temporal signal distances into spatial signal distances in topographic neural representations. This is achieved by neural dynamics of propagating waves, allowing current and former signals to interact spatiotemporally in the neural network. Within a biologically plausible framework, the TOM algorithm (1) reveals how dynamic neural networks can self-organize to embed spatial signals in temporal context in order to realize functional meaningful invariances, (2) predicts time-organized representational structures in cortical areas representing signals with systematic temporal relation, and (3) suggests that the strength with which signals interact in the cortex determines the type of signal topology realized in topographic maps (e.g., spatially or temporally defined signal topology). Moreover, the TOM algorithm supports the explanation of topographic reorganizations based on time-to-space transformations (Wiemer, Spengler, Joublin, Stagge, & Wacquant, 2000).     

A new method for expert target recognition system: Genetic wavelet extreme learning machine (GAWELM)

In last year’s, the expert target recognition has been become very important topic in radar literature. In this study, a target recognition system is introduced for expert target recognition (ATR) using radar target echo signals of High Range Resolution (HRR) radars. This study includes a combination of an adaptive feature extraction and classification using optimum wavelet entropy parameter values. The features used in this study are extracted from radar target echo signals. Herein, a genetic wavelet extreme learning machine classifier model (GAWELM) is developed for expert target recognition. The GAWELM composes of three stages. These stages of GAWELM are genetic algorithm, wavelet analysis and extreme learning machine (ELM) classifier. In previous studies of radar target recognition have shown that the learning speed of feedforward networks is in general much slower than required and it has been a major disadvantage. There are two important causes. These are: (1) the slow gradient-based learning algorithms are commonly used to train neural networks, and (2) all the parameters of the networks are fixed iteratively by using such learning algorithms. In this paper, a new learning algorithm named extreme learning machine (ELM) for single-hidden layer feedforward networks (SLFNs) Ahern et al., 1989, Al-Otum and Al-Sowayan, 2011, Avci et al., 2005a, Avci et al., 2005b, Biswal et al., 2009, Frigui et al., in press, Cao et al., 2010, Guo et al., 2011, Famili et al., 1997, Han and Huang, 2006, Huang et al., 2011, Huang et al., 2006, Huang and Siew, 2005, Huang et al., 2009, Jiang et al., 2011, Kubrusly and Levan, 2009, Le et al., 2011, Lhermitte et al., in press, Martínez-Martínez et al., 2011, Matlab, 2011, Nelson et al., 2002, Nejad and Zakeri, 2011, Tabib et al., 2009, Tang et al., 2011, which randomly choose hidden nodes and analytically determines the output weights of SLFNs, to eliminate the these disadvantages of feedforward networks for expert target recognition area. Then, the genetic algorithm (GA) stage is used for obtaining the feature extraction method and finding the optimum wavelet entropy parameter values. Herein, the optimal one of four variant feature extraction methods is obtained by using a genetic algorithm (GA). The four feature extraction methods proposed GAWELM model are discrete wavelet transform (DWT), discrete wavelet transform–short-time Fourier transform (DWT–STFT), discrete wavelet transform–Born–Jordan time–frequency transform (DWT–BJTFT), and discrete wavelet transform–Choi–Williams time–frequency transform (DWT–CWTFT). The discrete wavelet transform stage is performed for optimum feature extraction in the time–frequency domain. The discrete wavelet transform stage includes discrete wavelet transform and calculating of discrete wavelet entropies. The extreme learning machine (ELM) classifier is performed for evaluating the fitness function of the genetic algorithm and classification of radar targets. The performance of the developed GAWELM expert radar target recognition system is examined by using noisy real radar target echo signals. The applications results of the developed GAWELM expert radar target recognition system show that this GAWELM system is effective in rating real radar target echo signals. The correct classification rate of this GAWELM system is about 90% for radar target types used in this study.     

Fractional dual tree complex wavelet transform and its application to biometric security during communication and transmission

In this paper, the dual tree complex wavelet transform, which is an important tool and recent advancement in signal and image processing, has been generalized by coalescing dual tree complex wavelet transform and fractional Fourier transform. The new transform, i.e. the fractional dual tree complex wavelet transform (FrDT-CWT) inherits the excellent mathematical properties of dual tree complex wavelet transform and fractional Fourier transform. Possible applications of the proposed transform are in biometrics, image compression, image transmission, transient signal processing etc. In this paper, biometric is chosen as the primary application and hence a new technique is proposed for securing biometrics during communication and transmission over insecure channel.     

Adaptative time constants improve the prediction capability of recurrent neural networks

Classical statistical techniques for prediction reach their limitations in applications with nonlinearities in the data set; nevertheless, neural models can counteract these limitations. In this paper, we present a recurrent neural model where we associate an adaptative time constant to each neuron-like unit and a learning algorithm to train these dynamic recurrent networks. We test the network by training it to predict the Mackey-Glass chaotic signal. To evaluate the quality of the prediction, we computed the power spectra of the two signals and computed the associated fractional error. Results show that the introduction of adaptative time constants associated to each neuron of a recurrent network improves the quality of the prediction and the dynamical features of a neural model. The performance of such dynamic recurrent neural networks outperform time-delay neural networks.     

基于小波神经网络的大功率电器识别技术研究

针对公寓用电中的大功率电器识别问题,提出利用小波神经网络对大功率电器进行识别.由于采集到的电网电流信号是基波信号和谐波信号的混合,因此需要进行信号分离.基于Mallat快速算法进行小波变换提取其中的谐波电流信号;将总电流的平均功率增量和谐波电流的平均功率增量经过归一化处理后作为大功率电器识别的特征向量,利用得到的特征向量对融合型小波神经网络进行基于BP算法的网络训练;利用训练好的小波神经网络对未知的电网电流数据进行识别,实现大功率电器的在线识别和预警.对比仿真实验表明:利用小波神经网络对大功率电器识别比传统的BP神经网络有更高的准确率.     

基于小波变换和FRFT的图像加密算法

为了提高图像的安全性,增强图像的加密效果,提出一种基于离散小波和分数阶傅里叶变换（FRFT）的图像加密算法。首先利用离散小波变换使图像信号稀疏化,然后对稀疏化处理后的图像进行离散FRFT处理,得到最终加密图像。MATLAB的仿真结果表明,和单一的小波变换相比,该算法的加密和解密效果较好,能够较好地隐藏图片的信息。     

The fractional Fourier transform: theory, implementation and error analysis

The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications demand the implementation of the discrete fractional Fourier transform on a digital signal processor (DSP). The details of the implementation of the discrete fractional Fourier transform on ADSP-2192 are provided. The effect of finite register length on implementation of discrete fractional Fourier transform matrix is discussed in some detail. This is followed by the details of the implementation and a theoretical model for the fixed-point errors involved in the implementation of this algorithm. It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.     

一种基于聚类技术的选择性神经网络集成方法

神经网络集成是一种很流行的学习方法,通过组合每个神经网络的输出生成最后的预测、为了提高集成方法的有效性,不仅要求集成中的个体神经网络具有很高的正确率,而且要求这些网络在输入空间产生不相关的错误．然而,在现有的众多集成方法中,大都采用将训练的所有神经网络直接进行组合以形成集成,实际上生成的这些神经网络可能具有一定的相关性．为了进一步提高神经网络间的差异性,一种基于聚类技术的选择性神经网络集成方法CLU_ENN被提出．在获得个体神经网络后,并不直接对这些神经网络集成,而是先应用聚类算法对这些神经网络模型聚类以获得差异较大的部分神经网络;然后由部分神经网络构成集成;最后,通过实验研究了CLU_ENN集成方法,与传统的集成方法Bagging相比,该方法取得了更好的效果。     

Adaptive noise cancellation using enhanced dynamic fuzzy neural networks

In this paper, a novel adaptive noise cancellation algorithm using enhanced dynamic fuzzy neural networks (EDFNNs) is described. In the proposed algorithm, termed EDFNN learning algorithm, the number of radial basis function (RBF) neurons (fuzzy rules) and input-output space clustering is adaptively determined. Furthermore, the structure of the system and the parameters of the corresponding RBF units are trained online automatically and relatively rapid adaptation is attained. By virtue of the self-organizing mapping (SOM) and the recursive least square error (RLSE) estimator techniques, the proposed algorithm is suitable for real-time applications. Results of simulation studies using different noise sources and noise passage dynamics show that superior performance can be achieved.     

结合连续卷积算子的自适应加权目标跟踪算法

目的 在视觉跟踪领域中,特征的高效表达是鲁棒跟踪的关键,观察到在相关滤波跟踪中,不同卷积层表达了目标的不同方面特征,提出了一种结合连续卷积算子的自适应加权目标跟踪算法。方法 针对目标定位不准确的问题,提出连续卷积算子方法,将离散的位置估计转换成连续位置估计,使得位置定位更加准确;利用不同卷积层的特征表达,提高跟踪效果。首先利用深度卷积网络结构提取多层卷积特征,通过计算相关卷积响应大小,决定在下一帧特征融合时各层特征所占的权重,凸显优势特征,然后使用从不同层训练得到的相关滤波器与提取得到的特征进行相关运算,得到最终的响应图,响应图中最大值所在的位置便是目标所在的位置和尺度。结果 与目前较流行的3种目标跟踪算法在目标跟踪基准数据库（OTB-2013）中的50组视频序列进行测试,本文算法平均跟踪成功率达到85.4%。结论 本文算法在光照变化、尺度变化、背景杂波、目标旋转、遮挡和复杂环境下的跟踪具有较高的鲁棒性。